Development of the trailing shear layer in a starting jet during pinch-off

Abstract

AbstractExperiments on a circular starting jet generated by a piston–cylinder arrangement, over a range of Reynolds number from $2600$ to $5600$, are conducted so as to investigate the development of the trailing shear layer during the leading vortex ring formation, as well as the corresponding effects on the pinch-off process. Results obtained by digital particle image velocimetry (DPIV) show that secondary vortices start to develop in the trailing jet only after the critical time scale, the ‘formation number’, is achieved. The subsequent growth of the secondary vortices reduces the vorticity flux being fed into the leading vortex ring and, as a consequence, constrains the growth of leading vortex ring with larger circulation. Evolution of perturbation waves into secondary vortices is found to associate with growth and translation of the leading vortex ring during the formation process. A dimensionless parameter ‘$A$’, defined as ${\Gamma }_{\mathit{ring}} / ({x}_{\mathit{core}} \mrm{\Delta} U$), is therefore proposed to characterize the effect of the leading vortex ring on suppressing the nonlinear development of instability in the trailing shear layer, i.e. the initial roll-up of the secondary vortices. In a starting jet, $A$ follows a decreasing trend with the formation time ${t}^{\ensuremath{\ast} } $. A critical value ${A}_{c} = 1. 1\pm 0. 1$ is identified experimentally, which physically coincides with the initiation of the first secondary vortex roll-up and, therefore, indicates the onset of pinch-off process.